Working content > MacroModels

Our sensory experience of the world responds to a property of matter that we've mostly ignored in our discussion of motion -- heat and temperature. We all have a familiarity with things being hot or cold and we have a rich vocabulary to describe it.  As scientists have figured out what it means for an object to be hot or cold, the explanation has resolved a number of challenges to the Newtonian explanation of motion in a strange and interesting way. Although you probably know most of the results we will develop in this section, you may not have appreciated how strange some of them are!

A big challenge to the Newtonian theory of motion was the loss of mechanical energy due to non-conservative forces. Energy conservation seems like a very appealing idea. Why should some forces seem to destroy mechanical energy and others not? Why can we think of what some forces do as creating a potential energy and others not? 

I'm sure you already know the answer from previous science classes. Friction, viscosity, and drag steal coherent mechanical energy -- energy associated with the motion of all the molecules of an object moving together in the same way -- and move it into incoherent mechanical energy -- energy associated with the motion of the molecules of an object moving randomly in every which way. We call the latter thermal energy and we describe the increase in this energy as a rise in temperature.

But the strange part of the whole business is that we have a well developed intuition that "everything runs down." From our Newtonian perspective we see that this arises because there are always resistive forces that drain mechanical energy. If they are weak enough, we can ignore them for a time, but eventually, we expect, they will always win and motion will stop. But the reason that they stop is:

The reason that macroscopic mechanical energy appears to "run down" is because it gets transformed into thermal energy -- the random motion of the molecules of matter -- and, while that might be shifted around and transformed to other forms of energy, there is no mechanism that naturally "drains" thermal energy. It NEVER runs down.

So we are going to have to conclude that macro motion runs down because the energy of motion can be hidden in the temperature of objects. Now temperature appears to "run down" too, because hot things get cooler, but cold things warm up too. The real result, we shall find, is that thermal energy tends to get shared evenly -- but it never goes away. (I can even sometimes be transformed back to coherent mechanical energy -- a major topic of thermodynamics.) There is a new "total energy" -- coherent mechanical plus incoherent thermal; and we can restore a conservation of energy theorem! (There is also kinetic and potential energy internal to atoms and molecules as a result of the motion of their electrons. We call this chemical energy and discuss it in more detail elsewhere.)

The total coherent mechanical energy (kinetic plus potential) plus the total internal energy (thermal plus chemical) is conserved.

As we get to quantify how much thermal energy is in an object, we discover that this topic is another place where a careful analysis of the physics of what's going on leads us to see that we live on the small fringes of immense energies! Remember that we learned that matter -- which seems relatively inert -- it just sits there -- in fact consists of positive and negative charges which attract and repel each other with immense forces. Understanding those forces has led to the mastery of electrical energy and immense changes in the lives of human beings. Similarly, we will discover that the well down which our mechanical energy disappeared is a storehouse of huge thermal energies contained in every object. Understanding these energies led to the first industrial revolution (in the 19th century) and immense changes in the lives of human beings.

Follow ons:

• Measuring Temperature
• Heat capacity
• Heat transfer
• Biology of heat transfer

Resources: Mark W. Denny, Air and Water (Princeton U. Press, 1995). ch 8

Joe Redish and Karen Carleton 11/20/11

Joe Redish 12/1/12